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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A thin ring of mass 2 kg and radius r=140 mm is held against a frictionless wall by a 125-mm string AB. Determine (a) the distance d, (b) the tension in the string, (c) the reaction at C.

Expert Solution

Step 1

Given Data:

The mass of the thin ring is, $m = 2 kg$ .
The radius of the ring is, $r = 140 mm$ .
The length of the string AB is, $L = 125 mm$ .

Step 2

(a)

The given arrangement can be redrawn as below,

Step 3

The distance $d$ can be written as below,

$d = \sqrt{{(L + r)}^{2} - r^{2}}$

Substitute 125 mm for $L$ and 140 mm for $r$ in the above expression.

$\begin{array}{rcl} d & = & \sqrt{{(125 mm + 140 mm)}^{2} - {(140 mm)}^{2}} \\ = & 225 mm \end{array}$

Therefore, the distance $d$ is 225 mm.

Step 4

(b)

The expression for the weight of the thin ring can be written as below,

$W = m g$

Here, $g$ is the acceleration due to gravity which is equal to $9.81 m / s^{2}$ .

Substitute $9.81 m / s^{2}$ for $g$ and 2 kg for $m$ in the above expression.

$\begin{array}{rcl} W & = & (2 kg) (9.81 m / s^{2}) \\ = & 19.62 N \end{array}$

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